Method for Designing and Evaluating Eyeglass Lenses

Abstract

To provide a method for designing a spectacle lens and a method for evaluating a spectacle lens that can easily calculate the position of a central fovea and can acquire the optical performance of a lens on the basis of a visual axis.SOLUTION: A method for designing a lens, using a simulation by a computer device that causes a beam of light to pass through an eyeball model and a lens arranged in front of the model, includes: calculating positional data of a central fovea in the eyeball model by using data on an eye axis of the eyeball model; and acquiring optical performances of the lens on the basis of the obtained positional data of the central fovea and a beam of light that passes through a visual axis connecting joints, and designing the lens.SELECTED DRAWING: Figure 7

Description

Technical Field

[0001] The present invention relates to a method for designing and evaluating spectacle lenses and the like.

Background Art

[0002] In the design of spectacle lenses, when simulating lens characteristics such as refractive power and aberration by ray tracing using a computer device, it has conventionally been carried out on the premise that light rays pass through the eye rotation center point. The eye rotation center point is the center when the eyeball rotates and is the point through which the "optic axis" passes. However, in reality, the line of sight when looking at an object does not pass through the eye rotation center point. The axis through which the line of sight passes is called the "visual axis", and this visual axis passes through the fovea centralis where the visual acuity is the best. Patent Document 1 is shown as the prior art regarding the fovea centralis.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] In the conventional simulation, the reason for using the optic axis as a reference is mainly that it is computationally advantageous because the eye rotation center point, which is the rotation center of the eyeball model, can be used as the origin for calculation. However, in addition, the difference between the visual axis and the optic axis has not been considered so strictly, so it has been considered sufficient as a method for obtaining lens characteristics even assuming that the eye rotation center point is on the line of sight. On the other hand, when using the visual axis as a reference, the position of the fovea centralis must be calculated, which is computationally cumbersome. Furthermore, when using the optic axis length as a parameter when calculating the position of the fovea centralis, the calculation becomes even more cumbersome. However, in recent years, there has been a demand for customized optical characteristics in eyeglass lenses according to the user's vision, and more accurate optical performance of the lenses is desired. Therefore, in the design and evaluation of eyeglass lenses, a simulation based on the visual axis has been required again, and for this purpose, a method has been required that can easily calculate the position of the fovea centralis and obtain lens characteristics based on the visual axis. The present invention has been made by paying attention to such problems existing in the conventional technology. Its purpose is to provide a method for designing and evaluating an eyeglass lens that can easily calculate the position of the fovea centralis and obtain the optical performance of the lens based on the visual axis.

Means for Solving the Problems

[0005] As a first means for solving the above problems, it is a method for designing a lens using simulation by a computer device that transmits light rays to an eyeball model and a lens disposed in front of the eyeball model, wherein position data of the fovea centralis in the eyeball model is calculated using data on the eye axis of the eyeball model, and the optical performance of the lens is obtained based on the light ray passing through the visual axis connecting the obtained position data of the fovea centralis and the nodal point, and the lens is designed. Thereby, in the method for designing and evaluating an eyeglass lens by simulation, since the position data of the fovea centralis can be accurately calculated using clear data on the eye axis as position information, the optical performance of the lens can be obtained based on the light ray passing through the visual axis connecting the calculated position data of the fovea centralis and the nodal point, enabling simulation based on the visual axis, which has been cumbersome in the past, and enabling more accurate optical performance of the lens to be obtained.

[0006] "The optical performance of the lens" refers to the lens performance (characteristics) used in existing lens evaluations. For example, sphere power, cylinder power, equivalent spherical power (S + C / 2), astigmatism power and its axis, prism amount and its base value, addition power in progressive power lenses, aberration, distortion aberration, power error, etc. These performances can be used alone or in combination for design and evaluation. As the "eye model", for example, the measured eye data typified by Gullstrand's model eye may be used, or the eye rotation center may be simply set at a position about 24 to 29 mm away from the back surface of the lens. Since the distance from the back surface of the lens to the eye rotation center becomes longer in the case of axial myopia, etc., and the distance also varies when the position of the lens changes due to the height of the nose, it is preferable to set it according to the simulation conditions. The "eye axis" is the axis of the straight line passing through the eye rotation center and the nodal point of the eyeball. The "visual axis" is the axis of the straight line passing through the fovea centralis and the nodal point on the retina of the eyeball. In the simulation, the fixation point becomes the emission point of the point light source in the ray tracing, and the entire lens is simulated as the fixation point. The obtained optical characteristics are supplemented by interpolation calculation as necessary.

[0007] Also, as a second means, in the calculation of the visual axis, the calculation is performed based on the deviation of the axial direction angle between the eye axis and the visual axis. Both the visual axis and the eye axis pass through the nodal point. Although the eye axis passes through the eye rotation center, the visual axis does not pass through the eye rotation center. Therefore, it is possible to calculate the position data of the fovea centralis by applying the coordinates on the eye axis according to the difference in the angles of both. The angle of the visual axis with respect to the eye axis is deviated to the ear side and the lower side, respectively, and the deviation of the angle on the ear side is larger. Therefore, it is advisable to perform the calculation in consideration of at least the angle on the ear side. Also, as a third means, a fixation point passing through the visual axis is set on the two-dimensional plane at an arbitrary viewing distance, and when the visual axis passes through the fixation point, the position where the upper axis line passes through on the two-dimensional plane is taken as the intersection point, and the eye rotation amount is calculated based on the ray from the intersection point toward the eye rotation center, and the position data of the fovea centralis is calculated based on the calculated eye rotation amount. This is a method for calculating more specific fovea position data. That is, since the coordinates are clear for data based on the eye axis, a fixation point passing through the visual axis is set on a two-dimensional plane, and the intersection point connected by the eye axis corresponding to the visual axis on the two-dimensional plane is used. By this, it becomes possible to calculate the rotation amount of the eyeball model when the visual axis faces the fixation line by applying the eye torsion amount based on the eye axis. "The light ray from the intersection point toward the center of eye torsion" coincides with the axis line, becomes a straight line if there is no lens, and refracts at the lens surface and heads toward the center of eye torsion when there is a lens.

[0008] Also, as a fourth means, the eye torsion amount calculated at a third intersection point passing through the eye axis and intersecting the eyeball model is applied to calculate the fovea position data. The third intersection point assumes a point on the retina. Since the fovea is also a point on the retina, the accurate fovea on the visual axis can be calculated by giving the eye torsion amount to the third intersection point on the eye axis according to the angle of deviation between the eye axis and the visual axis. Also, as a fifth means, the eye torsion amount is calculated with the lens arranged in front of the eyeball model. As can be seen from this means, it is possible to calculate the fovea on the visual axis based on the data of the eye axis without installing the lens to be designed. However, due to the influence of the refractive power and aberration of the lens, the position of the actual fovea will deviate slightly compared to the case without installing the lens. Therefore, in order to pursue more accuracy, it is better to calculate with the lens to be designed arranged in front of the eyeball model.

[0009] As a sixth means, when calculating the eye torsion amount, a rotation matrix corresponding to the torsion amount is obtained, and the fovea position data is calculated based on the rotation matrix. As a method for calculating the amount of eye rotation that results in three-dimensional coordinate movement, it is most advisable to obtain a rotation matrix. By doing so, it becomes possible to apply the movement amount of the coordinates on the eye axis to the coordinates on the visual axis. Since the eyeball model uses the eye axis passing through the center of eye rotation as the rotation axis for the rotation matrix, for example, it is advisable to use the "Rodrigues rotation matrix" to streamline the calculation of the amount of eye rotation. Also, as a seventh means, in the calculation based on the deviation of the axial direction angle between the eye axis and the visual axis, different parameters are used for calculation according to the eye axis length. Since the angle formed by the eye axis and the visual axis varies depending on the eye axis length, it is advisable to calculate the angle using the eye axis length as a parameter. In particular, since the deviation angle of the visual axis with respect to the eye axis toward the ear side is large, it is advisable to adjust that deviation angle. For example, it is advisable to use an angle corrected considering the eye axis length using the following equations (1) or (2). In Equation 1, L is the average eye axis length and Δ is the change amount of the eye axis length. In Equation 2, SR is the spherical refractive power of the wearer's prescription, and reference is made to the measured values obtained with an ophthalmoscope such as an autorefractor or a phoropter. Note that applying Equation 1 using the eye axis length as a parameter is better because it can take into account the individual's eyeball model more than Equation 2 that simply considers the spherical refractive power of the prescription.

[0010]

Equation

[0011]

Equation

[0012] Also, as an eighth means, the lens is evaluated based on the optical performance of the lens obtained by computer simulation that evaluates the optical performance of the lens based on the optical performance obtained by any of the methods for designing spectacle lenses of the first to seventh means. In the present invention, for example, a designer of a spectacle manufacturer executes the design and evaluates the lens designed by the designer. In the present invention, for example, a designer of a spectacle manufacturer executes the design and also evaluates the lens. The invention of the present application is not limited to the configurations described in the following embodiments. The constituent elements of each embodiment and modification may be arbitrarily selected and combined. Also, any constituent element of each embodiment or modification may be arbitrarily combined with any constituent element described in the means for solving the invention or a constituent element embodying any constituent element described in the means for solving the invention. Regarding these, there is an intention to obtain rights in the amendment or divisional application of the present application, etc. Also, by filing a change application for a design application, there is an intention to obtain rights for the overall design or partial design. Although the drawings depict the entire device in solid lines, the drawings include not only the overall design but also partial designs claimed for a part of the device. For example, not only can a part of the members of the device be a partial design, but the drawings also include a partial design for a part of the device regardless of the members, such as a part of the members or a part of the member. As a part of the device, it may be a part of the members of the device or a part of the member.

Effects of the Invention

[0013] In the invention of the present application, since the position data of the fovea can be accurately calculated, the optical performance of the lens can be obtained based on the calculated position data of the fovea and the light ray passing through the visual axis connecting the node, enabling simulation based on the visual axis, which was conventionally troublesome, and more accurate optical performance of the lens can be obtained.

Brief Description of the Drawings

[0014]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Embodiments for Carrying Out the Invention

[0015] Hereinafter, specific embodiments will be described. FIG. 1 is a schematic block diagram of an arithmetic computer device 1 as an example for realizing the estimation method of the present invention. A monitor 2 as a display means or an output means, a printer 3, and an input device 4 such as a keyboard and a mouse are connected to the arithmetic computer device 1. The arithmetic computer device 1 is composed of a CPU (Central Processing Unit) 5 and peripheral devices such as a storage device 6. The CPU 5 executes processing based on various programs according to commands from the input device 4. The storage device 6 stores basic programs such as a program for controlling the operation of the CPU 5 and an OA processing program (for example, a Japanese input function and a printing function, etc.) for managing functions applicable to a plurality of programs in common. Further, shape data regarding the lens to be designed, and optical performance data calculated as a result of executing simulations of back surface ray tracing and transmitted light ray tracing for the lens with the shape data are stored.

[0016] As a process specialized for the present invention, the CPU 5 executes simulations of back surface ray tracing and transmitted light ray tracing based on the lens shape data by the simulation software stored in the storage device 6 along the visual axis. Further, as a result of executing the simulation according to the arithmetic program stored in the storage device 6, the CPU 5 creates an average diopter distribution diagram, an astigmatism distribution diagram, a prism distribution diagram, a distortion aberration distribution diagram, etc. by the contour drawing software based on the obtained data, and outputs them from the monitor 2 or the printer 3. Note that in the following calculations, it is not always necessary to execute them on a single arithmetic computer device 1. It may be executed on another arithmetic computer device 1 based on the result calculated on one arithmetic computer device 1.

[0017] Next, a specific example of the calculation of the visual axis and the simulation by ray tracing through the visual axis executed by the simulation software of the arithmetic computer device 1 will be specifically described with reference to FIGS. 2 to 7. Note that in actuality, the deviation angle between the visual axis and the eye axis is extremely small, but in the following description using the figures, the deviation angle between the visual axis and the eye axis is exaggerated for easy understanding. A. Calculation of the intersection point with respect to the designated fixation point As shown in FIG. 2, in the present embodiment, as the direction in which the visual axis points, first, a designated fixation point T is set (assumed) on a screen assumed at an arbitrary viewing distance position. If the visual axis is directed toward the designated fixation point T, the eye axis corresponding to the visual axis also passes through the screen. Therefore, in the simulation, the intersection points (Pr, Pl) of the left and right eye axes with the screen are obtained. (1) Regarding the calculation conditions The calculation conditions will be described with reference to FIG. 3. At this stage, the calculation is assumed without a lens. The light ray traveling direction is the X coordinate, the vertical direction orthogonal to this is the Y direction, and the left - right direction of the screen is the Z coordinate. Set the designated fixation point as T = (Z0, Y0) as shown in Fig. 2 (unit: mm). The viewing distance (distance from the midpoint between the pupils to the designated fixation point T) = D [mm] is a fixed value. With the midpoint between the pupils as the reference, the Z coordinate (Kz) of the eye rotation point in each eye is set as Kz = -PD / 2 [mm] for the left eye and Kz = +PD / 2 [mm] for the right eye (PD is the designated interpupillary distance). Assume that the eye rotation point K is a point on the horizontal line including the midpoint between the pupils.

[0018] (2) Calculation method (the calculation methods for the right eye and the left eye are the same) i) Regarding eye rotation, follow Listing's law, that is, "When the line of sight is directed to a certain third eye position (oblique direction), the rotation of the eyeball is uniquely determined by rotating the eye rotation axis (Listing's rotation axis) perpendicular to the plane (Listing's plane) including the line of sight at the first eye position (front) and the third eye position." (As shown in Fig. 4,) In Listing's plane according to Listing's law, the first eye position vector is set as the front view direction, and the third eye position vector is set as the eye rotation direction. The first eye position vector is G1(1, 0, 0), and the third eye position vector is G3(qx, qy, qz). These are unit vectors. The vector I of Listing's rotation axis according to Listing's law can be calculated as the cross product of G1 and G3. That is, I = G1 × G3 The eye rotation angle θi of such a Listing's rotation axis is calculated by the following formula (3).

[0019]

Equation

[0020] Using this eye rotation angle θi, obtain the Rodrigues rotation matrix L as the eye rotation matrix according to Listing's law. The rotation matrix L is shown by the following formula (4). Formula (4) shows the elements of vector I as (dx, dy, dz).

[0021]

Equation

[0022] (b) Based on the front view of FIG. 3, let the three-dimensional coordinates of node N be N = (Nx, Ny, Nz). If the distance from the eye rotation center, which is the origin, to the node is, for example, 5.6 mm, then node N is N = (5.6, 0, 0). Define the intersection point T0 = (D - Nx, 0, 0) of the visual axis and the screen with node N as the origin, and perform coordinate transformation to T0' by rotating α around the Y-axis and β around the Z-axis based on the deviation angles (α, β) of the visual axis with respect to the eye axis. Then, as shown in FIGS. 5(a) and 5(b), obtain the differences (ΔZ, ΔY) in the Z-coordinate and Y-coordinate between point T0 and point T0'. ΔY, ΔZ, and T0' are defined by Equation (5). When the visual axis points to any fixation point, assume that the deviation amount between the visual axis and the eye axis on the screen is always ΔY and ΔZ. However, when it is assumed that this assumption does not hold, it is possible to appropriately correct the non-compliance. Based on the specified fixation point T = (Z0, Y0) and the differences (ΔZ, ΔY), the intersection points P(Pr, Pl) = (Px, Py, Pz) of the eye axis and the screen when the visual axis with the eye rotation point as the origin points to the fixation point T can be obtained according to Equation (6) below. Note that the signs of the coordinates such as α, β, ΔZ, ΔY, Z0, Y0, Py, and Pz are appropriately changed according to the coordinate system shown in FIG. 5.

[0023]

Equation

[0024]

Equation

[0025] B. As shown in FIG. 6, the direction of the visual axis from the center of eye rotation to the intersection point, that is, the third eye position vector, is clear. The third eye position vector is (Y0 - ΔY) / D in the Y coordinate and ((Z0 - Kz) - ΔZ) / D in the Z coordinate. FIG. 6 illustrates the relationship between the visual axis and the optical axis on the Z coordinate side. Here, according to Listing's law based on the emitted ray from the back surface of the lens when the optical axis faces the intersection point, the nodal point is coordinate-transformed from N → N'. Assuming the emitted ray from the intersection point (Pr, Pl) whose coordinates were calculated in A. toward eye rotation with the lens to be designed or evaluated mounted on the left and right eyes, the eye rotation amount is obtained as the rotation matrix L from the first eye position vector G1 at the front view and the third eye position vector G3 based on the emitted ray from the back surface of the lens. Here, θi is obtained again based on the above equation (3), and the coordinate P in the three-dimensional space with the eye rotation as the origin is transformed into the coordinate P' after being rotated in the third eye position direction. That is, it is the following equation (7). The rotation matrix L is the Rodrigues rotation matrix L of the above equation (4).

[0026]

Equation

[0027] C. Using the rotation matrix L obtained in B., the initial fovea (Fr, Fl) is coordinate-transformed. Thereby, the fovea (Fr', Fl') when the visual axes of the left and right eyes are directed toward the fixation point T is determined. This transformation is calculated as follows. Here, the calculation is performed taking the right eye as an example. i) Assuming the direction of the first eye position, that is, the front view, consider the point F0(16.5, 0, 0) on the optical axis with the nodal point as the origin. Here, the x coordinate means the distance of 16.5 mm from the nodal point to the retina. However, when applying Equation (1), in order to consider the deviation Δ with respect to the standard eye axis length of the wearer, it is defined as the point F0(16.5 + Δ, 0, 0) accordingly. ii) As shown in FIG. 2, coordinate-transform F0 by the deviation angle α on the ear side and the deviation angle β on the lower side to obtain the initial fovea position F. The initial fovea position F corresponds to the third intersection point. This calculation is based on the following equation (8). Using a coordinate transformation that rotates the Y-axis considering the deviation angle α (rotation matrix Y(α)), F0 is rotated toward the ear side, and then, using a coordinate transformation that rotates the Z-axis considering the deviation angle β (rotation matrix Z(β)), F0 is rotated toward the subretinal side. This is because, based on the nodal point, the fovea is deviated by α toward the ear side and by β toward the lower side with respect to the eye axis. In the case of the left eye, the deviation angle α becomes negative, and the sign of sin(α) in the rotation matrix Z(α) changes.

[0028]

Equation

[0029] c) As shown in FIG. 7, using the rotation matrix L, the initial fovea position F(Fr, Fl) in (b) above is coordinate-transformed in the specified third eye position direction to obtain the fovea position F'(Fr', Fl') when the visual axis is directed toward the fixation point T. That is, the following Equation 9 is used. The rotation matrix L is the Rodrigues rotation matrix L of Equation 4 above. At this time, since the origin is changed from the nodal point to the eye rotation point, the distance from the nodal point to the eye rotation point (fixed at 5.6 mm in the embodiment) is subtracted from the x coordinate of the fovea position F before the coordinate transformation.

[0030]

Equation

[0031] Since the positions of the foveae (Fr', Fl') when the lines of sight of the left and right eyes are directed toward the fixation point T by D.C. have been obtained, considering the chief rays from the fixation point T toward the foveae (Fr', Fl') with the lenses to be designed or evaluated mounted on the left and right eyes, the lens powers (S, C, AX, Prism / Base, etc.) in each eye when looking at the fixation point T are calculated. More specifically i) The principal ray passes through the lens from the fixation point T and reaches the fovea (Fr', Fl'). Calculate the incident angle of the principal ray (the incident angle from the fixation point to the lens surface). When calculating, consider the refraction at the front and back surfaces of the lens and adjust the incident angle so that it reaches the fovea. ii) Set the secondary rays at intervals of 1 degree at positions 2 mm away from the position of the fixation point of the principal ray (i.e., the pupil diameter), and let them pass through the lens in the same way as the principal ray with the incident angle in i). iii) Calculate the distance (focal length f: unit mm) from the principal ray and two pairs of secondary rays to the position where they reach the back surface of the lens and are closest, and obtain the lens power from 1000. / f. The maximum lens power is S diopters, and the minimum lens power is S + C diopters.

[0032] By configuring as described above, the method of the embodiment has the following effects. (1) Since the position of the fovea (Fr', Fl'), which is unclear in terms of coordinates, is obtained based on the deviation angle from the clearly defined intersection points (Pr, Pl), nodal points, and eye rotation points that pass through the eye axis, ray tracing can be performed using the visual axis, which is the original way of seeing, and the visual state of the user can be verified more accurately. (2) By performing coordinate transformation using a rotation matrix until the calculation of the fovea (Fr', Fl'), accurate and optimal calculations can be performed for the rotating eye model.

[0033] The above embodiments are merely described as specific embodiments for exemplifying the principles and concepts of the present invention. That is, the present invention is not limited to the above embodiments. The present invention can also be embodied in a modified form as follows, for example. · The above embodiment is an example. In the calculation, it may be calculated in an order other than the above. · In the above, points with optical meanings such as nodal points and eye rotation points were directly used for calculation, but the nodal points and eye rotation points may be obtained indirectly for calculation. · In order to obtain the intersection point (Pr, Pl), in the above embodiment, as an example, a calculation method assuming a front view was given, but it may be obtained by calculation based on the designated fixation point T. · In the simulation, the lens to be designed or evaluated for wearing may be any lens as long as it is used as an eyeglass lens. For example, a spherical lens, an aspherical lens, a progressive power lens, etc. can be used. · In the above, in order to simplify the calculation, the deviation angles α and β used were average angles, but the deviation angles α and β may be appropriately changed and simulated assuming the axial length of the wearer's eyes.

Claims

1. Using simulation by a computer device that transmits light rays to an eyeball model and a lens disposed in front of the eyeball model, using data on the eye axis passing through the center of rotation of the eye and the nodal point of the eyeball model to calculate the position data of the fovea centralis in the eyeball model, and obtaining the optical performance of the lens based on the light ray on the visual axis passing through the obtained fovea centralis and the nodal point to design the lens. A method for designing a spectacle lens, comprising: setting a fixation point passing through the visual axis on a two-dimensional plane at an arbitrary viewing distance, taking the position where the eye axis passes through the two-dimensional plane when the line of sight passes through the fixation point as an intersection point, calculating the amount of eye rotation according to the axial angle deviation between the eye axis and the visual axis, calculating the position data of the fovea centralis based on the calculated amount of eye rotation, and calculating using different parameters according to the axial length of the wearer's eye axis when calculating the position data of the fovea centralis. A method for designing a spectacle lens, characterized in that.

2. Moving the intersection point according to the axial angle deviation between the eye axis and the visual axis, obtaining the difference between the position of the intersection point after movement and the intersection point before movement, and calculating the amount of eye rotation based on the difference. The method for designing a spectacle lens according to claim 1, characterized in that.

3. Applying the calculated amount of eye rotation to the initial position of the fovea centralis passing through the eye axis and intersecting the eyeball model to calculate the position data of the fovea centralis. The method for designing a spectacle lens according to claim 1 or 2, characterized in that.

4. Calculating the amount of eye rotation with the lens disposed in front of the eyeball model. The method for designing a spectacle lens according to any one of claims 1 to 3, characterized in that.

5. When calculating the position data of the fovea centralis, obtaining a rotation matrix corresponding to the amount of rotation, and calculating the position data of the fovea centralis based on the rotation matrix. The method for designing a spectacle lens according to any one of claims 1 to 4, characterized in that.

6. Evaluating a lens based on the optical performance obtained by the method for designing a spectacle lens according to any one of claims 1 to 5. A method for evaluating a spectacle lens, characterized in that.

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